Ratnesh and Vineet worked on alternate days, starting with Ratnesh. The entire work got completed in 54 days. If Ratnesh alone can finish the work in 48 days, then in how many days can Vineet alone do the work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 64.
We know that,
Ratnesh and Vineet worked on alternate days, starting with Ratnesh.
Hence, Ratnesh worked for 27 days and Vineet worked for 27 days.
Total work (LCM of 54 and 48) = 432 units [Not taking the fraction part of 54]
Efficiency of Ratnesh = 432/48 = 9 units/day
We know that when working on alternate days Ratnesh worked for 27 days
Total work done by Ratnesh = 9 × 27.75 = 249.75 units
Remaining work = 432 - 249.75 = 182.25 units
The remaining work is done by Vineet in 27 days
Efficiency of Vineet = 182.25/27 = 6.75 units/day
Hence, Vineet can complete the whole work alone = 432/6.75 = 64 days